Yes. What you are feeling is grief, and it is the ordinary, expected, proportional response to losing someone you loved. The species of the someone does not change that.
The reason it can feel like too much — like something is wrong with you for being this undone — is rarely the grief itself. It is the silence around it. There is no bereavement leave for a dog. No casseroles arrive. People who would sit with you for a week if a person died will ask, a few days in, whether you are thinking about getting another one.
That gap between what you feel and what the world treats as reasonable has a name: disenfranchised grief. Grief that the people around you don’t recognize as real, so you end up carrying it alone, and quietly start to wonder if your own heart is the thing that’s broken.
It isn’t. The bond was real. An animal is woven into the small, wordless hours of your life in a way most people never are — the morning routine, the spot on the bed, the body that was simply there, asking nothing, every single day. When that is gone, the day has holes in it where they used to be. Of course it hurts this much. You are not grieving too hard. You are grieving exactly as hard as you loved.